A self-consistent Ornstein-Zernike jellium for highly charged colloids (microgels) in suspensions with added salt.

This work discusses a jellium scheme, built within the framework of the multicomponent Ornstein-Zernike (OZ) equation, which is capable of describing the collective structure of suspensions of highly charged colloids with added salt, even in the presence of finite-size multivalent microions. This approach uses a suitable approximation to decouple the microion-microion correlations from the macroion-microion profiles, which in combination with the methodology from the dressed ion theory (DIT) gives a full account of the electrostatic effective potential among the colloids. The main advantages of the present contribution reside in its ability to manage the short-range potentials and non-linear correlations among the microions, as well as its realistic characterization of the ionic clouds surrounding each macroion. The structure factors predicted by this jellium scheme are contrasted with previously reported experimental results for microgel suspensions with monovalent salts (2019Phys. Rev. E100032602), thus validating its high accuracy in these situations. The present theoretical analysis is then extended to microgel suspensions with multivalent salts, which reveals the prominent influence of the counterion valence on the makeup of the effective potentials. Although the induced differences may be difficult to identify through the mesoscopic structure, our results suggest that the microgel collapsing transition may be used to enhance these distinct effects, thus giving a feasible experimental probe for these phenomena.

Effects of the curvature gradient on the distribution and diffusion of colloids confined to surfaces.

The properties and behavior of colloids confined to move on curved surfaces offer a fertile ground for analysis since the geometric constraints induce specific features that are not available in flat spaces. Given their pertinence for biological and physicochemical processes, both with potential useful applications, the development of the concepts and methodology necessary for a deeper understanding of these unconventional systems is indeed an essential pursuit. The present study discusses a general and rigorous algorithm for the implementation of Brownian dynamics simulations that solves underlying difficulties and shortcomings inherent to conventional first-order schemes. Still based on the Ermak-McCammon recipe, our approach complements it with the higher-order geodesical projections of the elementary jumps generated on the associated tangent plane. This strategy, which warrants the locally isotropic propagation of non-interacting particles, is tested with a model system of colloidal particles interacting through a screened Coulomb potential while confined to move on ellipsoidal surfaces. This allows us to measure the effects prompted by the curvature gradient on the static and dynamic properties of this system. The varying curvature thus induces energetically favorable configurations in which the particles maximize their Euclidean distancing by crowding the regions with the largest Gaussian curvature, while withdrawing from those with the lowest. In turn, these inhomogeneous distributions provoke the anisotropic self-diffusion of the confined colloids, which is examined by exploiting the pertinent geodesic radial coordinates. The proficient methods under consideration thus allows dealing with the rich and remarkable new phenomena generated by any distinctive surface geometry.

Volume transition effects on the correlations and effective interactions among highly charged microgels.

Recent experimental studies have demonstrated the huge influence that the volume phase transition (VPT) has on the collective structure of highly charged thermo-responsive microgels in aqueous solution with low concentrations of added monovalent salt, thus opening a promising new route for controlling the overall properties of practical colloidal suspensions. We present here an analysis of this structure based on the effective electrostatic potential obtained with the exact methodology of the dressed ion theory (DIT). Starting with a description at the primitive model level, we determine the correlations among the components of our model system (macroions plus monovalent anions and cations) by utilizing the two-density integral equation theory, thus allowing us to consider realistic values for the microgel charges. The resulting microgel structure factors show a good agreement with the reported light scattering measurements, whereas the microscopic pair distributions reveal that in this regime the shrunken states promote an enhanced counterion absorption into the microgels. This packing of counterions inside the microgels induces strongly non-linear correlations among the microions, and in turn provokes a substantial weakening of the microgel-microgel correlations. The ensuing effective interactions are then obtained by contracting the description to the level in which only the macroions are present. We find not only that the magnitude and reach of the corresponding pair potentials are markedly inhibited in the shrunken states, but also that their general form diverges from the conventional screened Coulomb shape. This makes it necessary to rethink the concepts of effective charge and screening length.

Accounting for effective interactions among charged microgels.

We introduce a theoretical approach to describe structural correlations among charged permeable spheres at finite particle concentrations. This theory explicitly accounts for correlations among microions and between microions and macroions and allows for the proposal of an effective interaction among macroions that successfully captures structural correlations observed in poly-N-isopropyl acrylamide microgel systems. In our description the bare charge is fixed and independent of the microgel size, the microgel concentration, and the ionic strength, which contrasts with results obtained using linear response approximations, where the bare charge needs to be adapted to properly account for microgel correlations obtained at different conditions.

Nanoparticles confined to a spherical surface in the presence of an external field: Interaction forces and induced microstructure.

The structural response of a set of charged nanoparticles confined to move on a spherical surface under the influence of an external field is studied by Brownian Dynamics (BD) simulations and by an integral equation approach (IEA). Considering an identical nanoparticle as the source of the external field, we analyze the force exerted by the N confined particles on the external one, as well as the corresponding potential energy, focusing on their dependence on the distance of the external particle to the center of the sphere r0. The connection of the force and potential to the equilibrium local distribution of the adsorbed particles, that is, the microstructure within the spherical monolayer induced by the external nanoparticle, which is also dependent on r0, is elucidated by this analysis. It is found that the external particle needs to surmount a considerable potential barrier when moving toward the spherical surface, although much smaller than the one generated by a uniform surface distribution with an equivalent amount of charge. This is understood in terms of the correlation hole within the confined monolayer induced by the external particle. Another interesting conclusion is that the IEA provides an accurate, almost quantitative, description of the main features observed in the BD results, yet it is much less computationally demanding. The connection of these results with the overall chemical equilibrium of charged surfactant nanoparticles in the context of Pickering emulsions is also briefly discussed.

Evidence of electrostatic-enhanced depletion attraction in the structural properties and phase behavior of binary charged colloidal suspensions.

In this paper we study the structure and phase behavior of binary mixtures of charged particles at low ionic strength. Due to the large size asymmetry between both species, light scattering measurements give us access only to the partial static structure factor that corresponds to the big particles. We observe that the addition of small charged colloids produces a decrease of the main peak of the measured static structure factor and a shift to larger scattering vector values. This finding is in agreement with theory based on integral equations with the Hypernetted-Chain Closure (HNC) relation. The effective interaction between two big particles due to the presence of small particles is obtained by a HNC inversion scheme and used in numerical simulations that adequately reproduce the experiments. We find that the presence of small particles induces an electrostatic depletion screening among the big colloids, creating around them an exclusion zone for the small charged colloids greater than that caused in the case of neutral small colloids, which in turn augments the depletion effect.

Structural and dynamic inhomogeneities induced by curvature gradients in elliptic colloidal halos of paramagnetic particles.

Paramagnetic colloidal particles distributed along an ellipse are used as a model system to study the effects of curvature gradients on the structure and dynamics of colloids in curved manifolds. Unlike what happens for circular and spherical systems, in the present case, the equilibrium one-particle distribution function displays inhomogeneities due to the changing curvature along the ellipse. The ensuing effects on the two-body correlations are also analyzed, leading to the observation of anisotropic and long-ranged effects. Another noticeable consequence is the slowing down of the self-diffusion of these particles, which for large eccentricities may induce metastable states; this is evaluated by means of the time-dependent self-distribution.

Effective electrostatic interactions among charged thermo-responsive microgels immersed in a simple electrolyte.

This work explores the nature and thermodynamic behavior of the effective electrostatic interactions among charged microgels immersed in a simple electrolyte, taking special interest in the effects due to the thermally induced variation of the microgel size while the remaining parameters (microgel charge and concentration, plus the amount of added salt) are kept constant. To this end, the rigorous approach obtained from applying the precise methodology of the dressed ion theory to the proper definition of the effective direct correlation functions, which emerge from tracing-out the degrees of freedom of the microscopic ions, is employed to provide an exact description of the parameters characterizing such interactions: screening length, effective permittivity, and renormalized charges. A model solution with three components is assumed: large permeable anionic spheres for the microgels, plus small charged hard spheres of equal size for the monovalent cations and anions. The two-body correlations among the components of this model suspension, used as the input for the determination of the effective interaction parameters, are here calculated by using the hyper-netted chain approximation. It is then found that at finite microgel concentrations the values of these parameters change as the microgel size increases, even though the ionic strength of the supporting electrolyte and the bare charge of the microgels remain fixed during this process. The variation of the screening length, as well as that of the effective permittivity, is rather small, but still interesting in view of the fact that the corresponding Debye length stays constant. The renormalized charges, in contrast, increase markedly as the microgels swell. The ratio of the renormalized charge to the corresponding analytic result obtained in the context of an extended linear response theory allows us to introduce an effective charge that accounts for the non-linear effects induced by the short-ranged association of microions to the microgels. The behavior of these effective charges as a function of the amount of added salt and the macroion charge, size, and concentration reveals the interplay among all these system parameters.

An exact method to obtain effective electrostatic interactions from computer simulations: the case of effective charge amplification.

We discuss here an exact method to determine the parameters regulating the screened Coulomb interactions among spherical macroions immersed in a simple electrolyte. This approach provides rigorous definitions for the corresponding screening length, effective permittivity, and renormalized charges, and can be employed for precise and reliable calculations of these parameters within any scheme. In particular, we introduce a simple procedure for extracting this information from computer simulations. The viability of this approach is demonstrated by applying it to a three-component model system which includes anionic nanoparticles and monovalent cations and anions. The mean forces between nanoparticles are determined directly from simulations with two macroions, plus small ions, inside a single cell with periodic boundary conditions. The values of the parameters of interest, on the other hand, are gathered from two separate sets of computer simulations: one set provides information about the short-range correlations among the small ions, which in turn determine the screening length and effective permittivity; the second set supplies the short-range components of the ionic distribution around one isolated macroion, which also determine its renormalized charge. The method presented here thus avoids the uncertain fitting of these parameters from the asymptotic tail of the mean force and allows us to investigate in detail this connection between the renormalized charge of the macroion and the short-range (virtual) part of the ionic cloud surrounding it. Using the standard prescription to extract an effective charge from the corresponding renormalized value, we then proceed to clarify the mechanisms behind the possibility of effective charge amplification (i.e., an effective charge larger than the bare macroion charge). Complementarily, we report results for the corresponding bridge functions too.

Formation and structure of colloidal halos in two-dimensional suspensions of paramagnetic particles.

Different Monte Carlo simulation approaches are used here to study the static structure induced by a spherical neutral substrate inserted in the midst of a two-dimensional suspension of paramagnetic particles. It is then observed that in some instances some of these particles are adsorbed to the surface of the substrate, forming colloidal halos. We investigate the necessary conditions for the formation of these halos and the dependence of the number of adsorbed particles on the relevant parameters of the system. The angular distribution of the adsorbed particles around the perimeter of the substrate is analyzed here too.

Charge renormalization of nanoparticles immersed in a molecular electrolyte.

The renormalization of the electric charge of nanoparticles (small colloids) at infinite dilution immersed in a supporting electrolyte containing molecular ions is studied here using a simple model. The nanoparticles are represented by charged spheres of finite diameter, the anions are assumed to be pointlike, and the cations are modeled as two identical charged points connected by a rigid rod. The static structure of this model system is determined using the reference interaction site model equations with suitable closure relations and the renormalized charges are analyzed employing the dressed interactions site theory approach. It is found that for a wide range of ionic strengths these renormalized charges are clearly dependent on the length of the cations for nanoparticles with negative bare charge, but this dependence is practically negligible for nanoparticles with positive bare charges. In the limit of zero cation length and small nanoparticle charges the standard Derjaguin-Landau-Verwey-Overbeek model renormalization is recovered. A brief account of the structural and thermodynamic properties of the model molecular electrolyte is also provided.

Asymmetric charge renormalization for nanoparticles in aqueous media.

The effective renormalized charge of nanoparticles in an aqueous electrolyte is essential to determine their solubility. By using a molecular model for the supporting aqueous electrolyte, we find that the effective renormalized charge of the nanoparticles is strongly dependent on the sign of the bare charge. Negatively charged nanoparticles have a lower effective renormalized charge than positively charged nanoparticles. The degree of asymmetry is a nonmonotonic function of the bare charge of the nanoparticle. We show that the effect is due to the asymmetric charge distribution of the water molecules, which we model using a simple three-site molecular structure of point charges.

Two-body correlations among particles confined to a spherical surface: packing effects.

The two-point correlation functions among particles confined to move within a spherical two-dimensional space are studied here using Monte Carlo simulations in the canonical ensemble and the corresponding liquid theory concepts. This work takes a simple model system with soft-sphere interactions among the particles lying on the spherical surface. We focus this study on the ordering induced by the particle packing and the restrictions imposed by the system topology. The corresponding grand canonical results are obtained from the canonical Monte Carlo data using the standard statistical mechanics formulas. These grand canonical ensemble results show that as the strength of the interactions increases, the system transits between liquidlike states and crystal-like states as the average number of particles on the spherical surface matches certain specific values. The crystal-like states correspond to sharp minima in the plot of the standard deviation in the number of particles on the spherical surface versus the average value of this number. We also test the validity of the integral equation approaches for this kind of closed but boundless systems: It is found that the Percus-Yevick approximation overestimates the correlations for this system in a liquid state, whereas the hypernetted-chain approximation underestimates these correlations.

A simple phenomenological fix for the dielectric constant within the reference interaction site model approach.

The effective interactions among ions immersed in water are studied by means of the effective pair potentials (EPPs) [J. Chem. Phys. 2002, 117, 6133] obtained after contracting (integrating out) the degrees of freedom of the solvent molecules. The dressed interaction site theory (DIST) leads to a simple way of adjusting the effective dielectric constant of the model solvent to its experimental value at standard conditions. The molecular structure of the solvent is mirrored in the structure of the short-ranged component of the induced EPPs, with noticeable differences between the cases with trivial (ideal gas) and nontrivial (experimental) values of the dielectric constant. The shape of these EPPs remains almost invariant over the whole range of salt concentrations considered here. The asymptotic behavior of the EPP between two macroions obtained after contracting the supporting electrolyte (water molecules plus small ions) is also briefly discussed.

A reference interaction site model approach to depletion forces induced by hard rodlike particles.

We study the effective interactions among large hard spherical colloidal particles induced by small hard rodlike particles and compare them with those induced by small hard spherical particles to highlight the specific effects due to the anisotropic shape of the former. This is done by determining the effective pair potentials within the framework of the reference interaction site model approach. The rodlike particles are modeled as N nonoverlapping spherical units arranged in a straight line, so that their total length is N times their transversal diameter. These results are compared against those obtained in the Asakura-Oosawa limit.

Molecular multivalent electrolytes: microstructure and screening lengths.

We study small rod-like molecular electrolytes solutions with their corresponding atomic counterions. The asymptotic length scales (decay length and wavelength) of the structural correlations are analyzed using the formalism of the dressed interaction site theory (DIST). The correlation functions are determined using the reference interaction site model equation complemented with a mixed approach in which the hypernetted-chain closure is used for the repulsive interactions, and the mean spherical approximation is used for the attractive interactions. The results from this scheme are in good agreement with the Monte Carlo computer simulations reported here. The asymptotic properties of the correlation functions of this molecular system are compared against those corresponding to two related simple (atomic) electrolyte models. The main conclusion is that the molecular structure of the ions lowers by two orders of magnitude the concentration at which the transition from monotonic to oscillatory decay occurs.

Energetic contributions to wall-particle depletion forces.

Recently, depletion forces were accounted for by a contraction of the description based on the integral equations theory of simple liquids [Phys. Rev. E 61, 4095 (2000)]. The extension of those results to the case of inhomogeneous systems is reported here. Besides, the energetic contributions to the wall-particle depletion forces are studied, as they arise as soon as charge is put on some of the components of a binary mixture of hard spheres on the front of a hard wall. By charging the small particles the amplitude of the depletion attraction between wall and large particles is reduced, and can even become a repulsion. A similar effect is observed if an attractive interaction between wall and small particles is present.